Signals representing blood velocity may be derived by transmitting successive bursts of a few cycles of acoustic carrier wave along each of a plurality of radial lines with an electro-acoustic transducer and sampling the electrical signals produced by echos reflected from targets along the line at intervals separated by one quarter of the period of the carrier wave so as to drive an in phase quadrature component I and a quadrature phase quadrature component Q. The arc-tangent of I/Q is the angle between the components. In accordance with the Doppler principle, the acoustic wave impinging on the transducer will have the same frequency as the carrier wave so as to produce an angle of 90 degrees if the reflection is from a stationary target, a greater frequency than the carrier wave so as to produce an angle greater than 90 degrees if the target is moving toward the transducer and a lesser frequency than the carrier wave so as to produce an angle less than 90 degrees if the target is moving away from the transducer. The change in the angle of reflection from a target on an successive transmission is therefore an indication of the Doppler frequency shift from which the velocity of the target can be determined.
In apparatus described by Brandestini in an article entitled TOPOFLOW-A DIGITAL FULL RANGE DOPPLER VELOCITY METER and published in the September 1978 issue of IEEE Transactions on Sonics and Ultrasonics, an estimate of the velocity of target is determined from an average of the angles acquired from samples of its reflections of a plurality of acoustic pulses transmitted along the same line.
Because this does not take into account the amplitude of the reflection, the velocity so attained is not the average velocity. The straight forward way of attaining the average velocity would be to carry out the function of the following equation in which S(w) is the Fourier power spectrum of the sampled echo. ##EQU1## In this equation the magnitude of each frequency is multiplied by that frequency, the products are added together so as to derive the numerator and the denominator is the sum of the magnitudes. Whereas this can be done by using an FFT, it is expensive.
In apparatus described in a European patent application number 83104067.0 filed on 4/26/83, an average velocity is derived that is very close to the precise value by using autocorrelation techniques. In particular, the I and Q components of a sample of the reflection of one burst from a target are multiplied by the conjugate of the I and Q components of a sample of the reflection of the next burst from the same target. Thus if seven bursts are transmitted along a line, there are six multiplications. The real components of all multiplications are averaged as are the imaginary components. The angle having a tangent determined by the ratio of the average of imaginary components to the average of the real components resulting from the multiplications can be shown to correspond to the average or mean Doppler frequency, and this can be translated into the average velocity.
In practice the amplitude of one set of I and Q components can be much greater than the others due to factors not related to the velocity of particles of interest so that they can dominate the averages and introduce considerable error in the velocity.
In U.S. patent application bearing Ser. No. 06/765,897 filed on 8/14/85 and entitled "Pulsed Doppler Flow Mapping Apparatus", these problems are overcome, but both types of apparatus suffer from the need for multipliers having relatively large numbers of bits. This significantly increases the cost so that the usual design reduces the number of bits and suffers from a lack of accuracy.
At the present time there is doubt as to whether the latter approach or the Brandestini approach is to be preferred. In some situations, one is better than the other.